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The absorption of low-frequency noise has always been limited by structural thickness, but the novel physical properties of sound-absorbing metamaterials provide a solution to this problem. Based on genetic algorithm, an acoustic metasurface absorber (AMA) composed of micro-perforated plates (MPPs) and impedance matching coiled-up cavities (IMCCs) is proposed. Different from previously reported metamaterials, this structure can easily provide flexible and accurate broadband sound absorption in different target frequency bands. The theoretical model behind the algorithm is established, and two optimal structures (AMA I/AMA II) are obtained for low and mid-high frequency bands. Broadband sound absorption is realized with a thickness of only 71 mm (about 1/13 of the relevant wavelength at 369 Hz), and an average sound absorption coefficient of 0.931 is achieved in the low-frequency band of 350–1000 Hz. Furthermore, by changing the frequency band of the quasi-perfect absorber to 500–2000 Hz, the average sound absorption coefficient exceeds 0.945 with a thickness of only 55 mm (about 1/11 of the relevant wavelength at 563 Hz). The reflection coefficient in the complex plane and theoretical impedance analysis are utilized to reveal the underlying mechanism of the absorption and the acoustic characteristics of the two structures, which show excellent broadband absorption performance in the low and mid-high frequency bands. This work provides a method of arbitrarily modulating surface acoustic impedance in broadband and a reference for broadband noise control.